The four fraction rules
a/b − c/d = (ad − cb) / bd
a/b × c/d = ac / bd
a/b ÷ c/d = ad / bc (multiply by the reciprocal)
Addition and subtraction need a common denominator — multiplying the two denominators always works, and the calculator then reduces the answer. Multiplication is straight across; division flips the second fraction and multiplies.
Worked example
1/2 + 3/8: common denominator 8 → 1/2 = 4/8 → 4/8 + 3/8 = 7/8 = 0.875. With the general rule instead: (1×8 + 3×2) / (2×8) = 14/16, which reduces by their greatest common divisor 2 to the same 7/8.
Simplifying: the GCD
A fraction is in lowest terms when the numerator and denominator share no factor but 1. The calculator divides both by their greatest common divisor (found with Euclid's algorithm): 42/56 → GCD 14 → 3/4. Top-heavy results also appear as mixed numbers: 14/4 → 7/2 → 3 ½.
Fractions you'll meet constantly
| Fraction | Decimal | Percent |
|---|---|---|
| 1/8 | 0.125 | 12.5% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.333… | 33.3% |
| 3/8 | 0.375 | 37.5% |
| 1/2 | 0.5 | 50% |
| 5/8 | 0.625 | 62.5% |
| 2/3 | 0.667… | 66.7% |
| 3/4 | 0.75 | 75% |
| 7/8 | 0.875 | 87.5% |
Frequently asked questions
How do I add fractions with different denominators?
Rewrite both over a common denominator, then add the numerators. 1/2 + 3/8: since 8 is a multiple of 2, write 1/2 as 4/8, giving 7/8. When neither denominator divides the other, multiply them together and simplify at the end.
Why do you flip the second fraction when dividing?
Dividing by a number is the same as multiplying by its reciprocal — dividing by 1/2 asks 'how many halves fit?', which doubles the answer. So a/b ÷ c/d becomes a/b × d/c.
How do I simplify a fraction to lowest terms?
Divide top and bottom by their greatest common divisor. For 24/36, the GCD is 12, so it reduces to 2/3. Repeatedly dividing by any common factor (2, 3, …) reaches the same result.
How do I work with mixed numbers like 2 ¾?
Convert to an improper fraction first: 2 ¾ = (2×4 + 3)/4 = 11/4. Do the arithmetic, then convert back — this calculator shows the mixed form of any top-heavy answer automatically.
How do I turn a fraction into a decimal or percent?
Divide the numerator by the denominator: 5/8 = 0.625. Multiply by 100 for a percentage: 62.5%. Repeating decimals like 1/3 = 0.333… are the ones that can't be written exactly.